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Entropy
In thermodynamics, entropy (usual symbol S) is a measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder. According to the second law of thermodynamics the entropy of anisolated system never decreases; such a system will spontaneously evolve toward thermodynamic equilibrium, the configuration withmaximum entropy. Systems that are not isolated may decrease in entropy, provided they increase the entropy of their environment by at least that same amount. Since entropy is a state function, the change in the entropy of a system is the same for any process that goes from a given initial state to a given final state, whether the process is reversible or irreversible. However, irreversible processes increase the combined entropy of the system and its environment. Tossup Questions # A covariant bound on this quantity proposed by Raphael Bousso is defined in terms of this quantity's value on light-like hypersurfaces chosen so that the generating null geodesics have non-positive expansion. One argument against white holes' existence in our universe is the significantly lower value for this quantity they have than their black counterparts. The maximum value for this quantity in a region of radius R is equal to 2pi R times Boltzmann's constant times energy enclosed divided by h-bar times c, according to a bound put forth by Jacob (*) Bekenstein. The equality case in the Bekenstein bound is achieved by black holes, for which this quantity is proportional to area, as suggested by the observation that event horizons generally only grow in size. For 10 points, identify this quantity whose non-decrease is the subject of the second law of thermodynamics. # One version of this quantity is equal to the trace of the density matrix, and this quantity is the macroscopic quantity that characterizes the microcanonical ensemble. One equation states that this quantity is the product of Boltzmann's constant and the natural logarithm of the number of microstates of a system. The third law of thermodynamics states that this quantity is zero for a perfect crystal at absolute zero. For 10 points, name this thermodynamic quantity, higher for gases than for liquids or solids, the measure of disorder in a system. # One estimate for this quantity, equal to 10.5 times the ideal gas constant, breaks down for liquids with strong intermolecular forces, thus deviating from Trouton's rule. In one formulation, this quantity is proportional to the sum of the products of microstate probabilities and their respective natural logs. The change in this quantity can also be calculated as change in (*) heat divided by temperature. For an isolated system, this never-decreasing property has been challenged by Maxwell's Demon, but otherwise holds true according to the Second Law of Thermodynamics. For ten points, name this property that measures the disorder in a system. # In a reversible process, the change in this quantity for an ideal gas equals Cp times the log of the temperature ratio minus R times the log of the pressure ratio. Maxwell's relations relate the first partial derivatives of pressure, volume, temperature, and this quantity. For a reservoir absorbing heat, the change in this quantity equals the heat divided by the temperature of the reservoir. It is multiplied by temperature in a formula for Helmholtz free energy, and lost work can be attributed to increases in this quantity, which occurs for every spontaneous process according to the second law of thermodynamics. For 10 points, name this measurement of disorder symbolized S. # In a solid under the influence of an electric field, the production of this type of current in addition to the charge current causes the Peltier effect. Perelman introduced one form of this quantity that was both coercive and critical for Ricci flow. A strong magnetic field suppression of thermopower is an indication of a large contribution to this quantity due to spins. Another form of this quantity is based off power law generating statistics and uses a parameter q that quantifies how much this quantity departs from (*) extensivity. This quantity is one of the natural variables of both enthalpy and internal energy. The sum of the product of the eigenvalues of the density matrix with the log of those eigenvalues gives another form of this quantity. For 10 points, name this quantity whose most basic form is equal to Boltzmann's constant times the log of the number of microstates.